Coriolis flow meter and method for determining flow characteristics

ABSTRACT

A Coriolis flow meter ( 5 ) is provided according to an embodiment of the invention. The meter ( 5 ) includes one or more flow conduits ( 103 ), at least two pickoff sensors ( 105, 105 ′) affixed to the one or more flow conduits ( 103 ), a driver ( 104 ) configured to vibrate the one or more flow conduits ( 103 ), and meter electronics ( 20 ) coupled to the at least two pickoff sensors ( 105, 105 ′) and to the driver ( 104 ). The meter electronics ( 20 ) vibrate the one or more flow conduits ( 103 ) of the flow meter ( 5 ) with a first vibration frequency and in a first out-of-phase bending mode, measure a first vibrational response, with the first vibrational response being generated in response to the first vibration frequency, vibrate the one or more flow conduits ( 103 ) with at least a second vibration frequency and in the first out-of-phase bending mode, measure a second vibrational response, and determine at least a mass flow rate and a viscosity using the first and second vibrational responses.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a Coriolis flow meter and method fordetermining flow characteristics, and more particularly, to a Coriolisflow meter and method for determining flow characteristics using two ormore vibrational responses.

2. Statement of the Problem

Vibrating conduit sensors, such as Coriolis mass flow meters, typicallyoperate by detecting motion of a vibrating conduit that contains aflowing material. Properties associated with the material in theconduit, such as mass flow, density and the like, can be determined byprocessing measurement signals received from motion transducersassociated with the conduit. The vibration modes of the vibratingmaterial-filled system generally are affected by the combined mass,stiffness and damping characteristics of the containing conduit and thematerial contained therein.

A typical Coriolis mass flow meter includes one or more conduits thatare connected inline in a pipeline or other transport system and conveymaterial, e.g., fluids, slurries and the like, in the system. Eachconduit may be viewed as having a set of natural vibration modesincluding, for example, simple bending, torsional, radial, and coupledmodes. In a typical Coriolis mass flow measurement application, aconduit is excited in one or more vibration modes as a material flowsthrough the conduit, and motion of the conduit is measured at pointsspaced along the conduit. Excitation is typically provided by anactuator, e.g., an electromechanical device, such as a voice coil-typedriver, that perturbs the conduit in a periodic fashion. Mass flow ratemay be determined by measuring time delay or phase differences betweenmotions at the transducer locations. Two such transducers (or pickoffsensors) are typically employed in order to measure a vibrationalresponse of the flow conduit or conduits, and are typically located atpositions upstream and downstream of the actuator. The two pickoffsensors are connected to electronic instrumentation by cabling, such astwo independent pairs of wires. The instrumentation receives signalsfrom the two pickoff sensors and processes the signals in order toderive a mass flow rate measurement.

Traditional Coriolis mass flow meters provide continuous measurement ofthe mass flow rate, density, and temperature of the flow medium flowingthrough the flow meter. However, a change in any of the flowcharacteristics of the flow medium can cause an increase or decrease inthe mass loading on the flow meter, and hence will cause an error in theindicated density, among other things.

Designers of vibrating element transducers, such as Coriolis mass flowmeters or densitometers, generally try to maximize the sensitivity ofthe mass, density, and temperature while minimizing the transducersensitivity to the viscosity, VOS, shear rate, pressure, and Reynoldsnumber. As a result, a typical prior art flow meter is capable ofaccurately measuring the mass, density, and temperature but is notcapable of accurately measuring additional flow characteristics such asone or more of the viscosity, VOS, shear rate, pressure, and Reynoldsnumber. There is a need in flow meter applications to measure other flowcharacteristics in addition to mass, density, and temperature.

SUMMARY OF THE SOLUTION

The present invention helps solve the problems associated withdetermining flow characteristics of a flow meter.

A Coriolis flow meter is provided according to an embodiment of theinvention. The Coriolis flow meter comprises one or more flow conduits,at least two pickoff sensors affixed to the one or more flow conduits, adriver configured to vibrate the one or more flow conduits, and meterelectronics coupled to the at least two pickoff sensors and to thedriver. The meter electronics is configured to vibrate the one or moreflow conduits of the flow meter with a first vibration frequency and ina first out-of-phase bending mode, measure a first vibrationalresponsive the one or more flow conduits, with the first vibrationalresponse being generated in response to the first vibration frequency,vibrate the one or more flow conduits with at least a second vibrationfrequency and in the first out-of-phase bending mode, measure a secondvibrational response, with the second vibrational response beinggenerated in response to the second vibration frequency, and determineat least a mass flow rate and a viscosity using the first vibrationalresponse and the second vibrational response.

A method for determining flow characteristics in a Coriolis flow meteris provided according to an embodiment of the invention. The methodcomprises vibrating one or more flow conduits of the flow meter with afirst vibration frequency and in a first out-of-phase bending mode andmeasuring a first vibrational response of the one or more flow conduits.The first vibrational response is generated in response to the firstvibration frequency. The method further comprises vibrating the one ormore flow conduits with at least a second vibration frequency and in thefirst out-of-phase bending mode and measuring a second vibrationalresponse. The second vibrational response is generated in response tothe second vibration frequency. The method further comprises determiningat least a mass flow rate and a viscosity of the flow medium using thefirst vibrational response and the second vibrational response.

A Coriolis flow meter software product for determining flowcharacteristics in a Coriolis flow meter is provided according to anembodiment of the invention. The software product comprises a controlsoftware configured to direct a processing system to vibrate one or moreflow conduits of the flow meter with a first vibration frequency and ina first out-of-phase bending mode, measure a first vibrational responseof the one or more flow conduits, with the first vibrational responsebeing generated in response to the first vibration frequency, vibratethe one or more flow conduits with at least a second vibration frequencyand in the first out-of-phase bending mode, measure a second vibrationalresponse, with the second vibrational response being generated inresponse to the second vibration frequency, and determine at least amass flow rate and one or more flow characteristics using the firstvibrational response and the second vibrational response. The softwareproduct further comprises a storage system that stores the controlsoftware.

ASPECTS

In one aspect, the determining further comprises determining a density.

In another aspect, the determining further comprises determining a shearrate.

In yet another aspect, the determining further comprises determining aReynolds number.

In yet another aspect, the determining further comprises determining avelocity of sound (VOS).

In yet another aspect, the determining further comprises determining apressure.

In yet another aspect, the viscosity comprises a kinematic viscosity.

In yet another aspect, the viscosity comprises a dynamic viscosity.

In yet another aspect, the vibrating further comprises jumping betweenthe first vibration frequency and the second vibration frequency.

In yet another aspect, the vibrating further comprises substantiallysimultaneously vibrating the one or more flow conduits with the firstvibration frequency and the second vibration frequency.

In yet another aspect, the vibrating further comprises sweeping betweenthe first vibration frequency and the second vibration frequency over apredetermined sweep time period.

In yet another aspect, the first vibration frequency and the secondvibration frequency are substantially equally spaced above and below afundamental frequency of the one or more flow conduits.

In yet another aspect, the one or more flow conduits comprise twosubstantially U-shaped flow conduits.

DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a Coriolis flow meter comprising a flow meterassembly and meter electronics.

FIG. 2 shows meter electronics according to an embodiment of theinvention.

FIG. 3 is a flowchart of a method for determining flow characteristicsin a Coriolis flow meter according to an embodiment of the invention.

FIG. 4A shows magnitude response characteristics for three differentvalues of the damping factor ζ, while FIG. 4B shows the correspondingphase response characteristics.

FIG. 5 shows a feedback loop for controlling a vibration frequencyapplied to the flow meter assembly.

DETAILED DESCRIPTION OF THE INVENTION

FIGS. 1-5 and the following description depict specific examples toteach those skilled in the art how to make and use the best mode of theinvention. For the purpose of teaching inventive principles, someconventional aspects have been simplified or omitted. Those skilled inthe art will appreciate variations from these examples that fall withinthe scope of the invention. Those skilled in the art will appreciatethat the features described below can be combined in various ways toform multiple variations of the invention. As a result, the invention isnot limited to the specific examples described below, but only by theclaims and their equivalents.

FIG. 1 illustrates a Coriolis flow meter 5 comprising a flow meterassembly 10 and meter electronics 20. Meter electronics 20 is connectedto meter assembly 10 via leads 100 to provide density, mass flow rate,volume flow rate, totalized mass flow, temperature, and otherinformation over path 26.

Flow meter assembly 10 includes a pair of flanges 101 and 101′,manifolds 102 and 102′, driver 104, pick-off sensors 105-105′, and flowconduits 103A and 103B. Driver 104 and pick-off sensors 105 and 105′ areconnected to flow conduits 103A and 103B.

Flanges 101 and 101′ are affixed to manifolds 102 and 102′. Manifolds102 and 102′ are affixed to opposite ends of spacer 106. Spacer 106maintains the spacing between manifolds 102 and 102′ to preventundesired vibrations in flow conduits 103A and 103B. When flow meterassembly 10 is inserted into a pipeline system (not shown) which carriesthe material being measured, material enters flow meter assembly 10through flange 101, passes through inlet manifold 102 where the totalamount of material is directed to enter flow conduits 103A and 103B,flows through flow conduits 103A and 103B and back into outlet manifold102′ where it exits meter assembly 10 through flange 101′.

Flow conduits 103A and 103B are selected and appropriately mounted toinlet manifold 102 and outlet manifold 102′ so as to have substantiallythe same mass distribution, moments of inertia, and elastic modulesabout bending axes W-W and W′-W′ respectively. The flow conduits extendoutwardly from the manifolds in an essentially parallel fashion.

Flow conduits 103A-B are driven by driver 104 in opposite directionsabout their respective bending axes W and W′ and at what is termed thefirst out-of-phase bending mode of the flow meter. Driver 104 maycomprise one of many well known arrangements, such as a magnet mountedto flow conduit 103A and an opposing coil mounted to flow conduit 103B.An alternating current is passed through the opposing coil to cause bothconduits to oscillate. A suitable drive signal is applied by meterelectronics 20, via lead 110 to driver 104.

Meter electronics 20 transmits sensor signals on leads 111 and 111′,respectively. Meter electronics 20 produces a drive signal on lead 110which causes driver 104 to oscillate flow conduits 103A and 103B. Meterelectronics 20 processes left and right velocity signals from pick-offsensors 105 and 105′ in order to compute a mass flow rate. Path 26provides an input and an output means that allows meter electronics 20to interface with an operator. The description of FIG. 1 is providedmerely as an example of the operation of a Coriolis flow meter and isnot intended to limit the teaching of the present invention.

FIG. 2 shows meter electronics 20 according to an embodiment of theinvention. The meter electronics 20 includes a communication interface201, a processing system 202, and a storage system 203. The processingsystem 202 is coupled to the communication interface 201.

The communication interface 201 enables communications between the meterelectronics 20 and external devices. The communication interface 201enables transmission of computed flow characteristics to an externaldevice via the path 26. The external devices can include the flow meterassembly 10 (via the leads 100 of FIG. 1), a monitoring device ordevices (via the path 26 of FIG. 1), or any manner of user interface orcommunication device. The communication interface 201 enables thereceipt of flow measurements from the flow meter assembly 10 over theleads 100. The communication interface 201 can be capable of any mannerof electronic, optical, or wireless communication, for example. Theinterface 26 can enable communication over telephone systems and/ordigital data networks. Consequently, the meter electronics 20 cancommunicate with remote flow meters, remote processing/monitoringdevices, remote memory media, and/or remote users.

The processing system 202 conducts operations of the meter electronics20 and processes flow measurements from the flow meter assembly 10. Theprocessing system 202 executes a processing routine 210 and processesthe flow measurements in order to produce one or more flowcharacteristics. The processing system 202 can comprise a generalpurpose computer, a microprocessing system, a logic circuit, or someother general purpose or customized processing device. The processingsystem 202 can be distributed among multiple processing devices. Theprocessing system 202 can include any manner of integral or independentelectronic storage medium, such as the storage system 203.Alternatively, the storage system 203 can comprise an independentelectronic storage medium in communication with the processing system202.

The storage system 203 can store flow meter parameters and data,software routines, constant values, and variable values. In oneembodiment, the storage system 203 includes the processing routine 210that is executed by the processing system 202. The storage system 203stores variables used to operate the flow meter assembly 10. The storagesystem 203 in one embodiment stores variables such as a first vibrationfrequency 211, at least a second vibration frequency 212, a firstvibrational response 213, a second vibrational response 214, and a sweeptime period 215.

The storage system 203 stores one or more flow characteristics obtainedfrom the flow measurements. The storage system 203 in one embodimentstores flow characteristics such as a mass flow rate 220, a density 221,a kinematic viscosity 222, a dynamic viscosity 223, a shear rate 224, aReynolds number 225, a velocity of sound (VOS) 226, and a damping factor(or quality factor Q) 227. It should be understood that other flowcharacteristics can also be determined and recorded, such as temperatureand/or pressure, for example.

The mass flow rate 220 is a measurement of the mass flow through theflow meter assembly 10. The density 221 is the density of the flowmaterial in the flow meter assembly 10.

Viscosity of a fluid can be defined as a resistance of the fluid toshear or flow, and is a measure of the adhesive/cohesive properties ofthe fluid. This resistance is caused by intermolecular fiction exertedwhen a first fluid layer attempts to slide past another fluid layer. Ameasurement of the viscous property of a fluid is desirable in order toproperly design and operate equipment for pumping, measuring, orotherwise handling a fluid.

The kinematic viscosity 222 can be defined as a ratio of dynamicviscosity to the density. The kinematic viscosity 222 can be calculatedfrom the dynamic viscosity 223 and the density 221. The dynamicviscosity 223 can be defined as a tangential force per unit arearequired to move one horizontal plane with respect to the other at aunit velocity when maintained a unit distance apart by the fluid.

The shear rate 224 can be defined as the rate of change of velocity atwhich one layer of fluid passes over another fluid layer.

The Reynolds number 225 can be defined as a measure of the importance ofinertia to viscosity effects. At high Reynolds numbers, a flow maybecome turbulent, exhibiting qualitatively different behavior than thesame liquid at a low Reynolds number.

The VOS 226 is the speed of sound in the flow medium. The VOS 226 canchange with changes in the flow medium, can change with changes indensity in the flow medium, or can change with changes in thecomposition of the flow medium, for example.

The damping factor 227 can be defined as a measure of how damped thevibration is by the flow medium. Alternatively, the damping factor 227can be defined as a measure of the viscosity of the flow medium.

The processing system 202 executes the processing routine 210 in orderto determine the one or more flow characteristics. The processingroutine 210, when executed by the processing system 202, configures theprocessing system 202 to vibrate one or more flow conduits 103 of theflow meter 5 with the first vibration frequency 211, measure the firstvibrational response 213 of the one or more flow conduits 103, with thefirst vibrational response 213 being generated in response to the firstvibration frequency 211, vibrate the one or more flow conduits 103 withat least a second vibration frequency 212, measure a second vibrationalresponse 214, with the second vibrational response 214 being generatedin response to the second vibration frequency 212, and determine atleast the mass flow rate 220 and a viscosity of the flow medium usingthe first vibrational response 213 and the second vibrational response214 (see FIG. 3).

The first vibration frequency 211 and the second vibration frequency 212can comprise any desired frequencies. In one embodiment, the firstvibration frequency 211 and the second vibration frequency 212 aresubstantially equally spaced above and below a fundamental frequency ofthe flow meter assembly 10. However, other frequencies can be employed,depending on the flow medium and the ambient environment.

In one embodiment, the processing routine 210 can jump between the firstvibration frequency 211 and the second vibration frequency 212. In analternate embodiment, the processing routine 210 can substantiallysimultaneously vibrate the one or more flow conduits 103 with the firstvibration frequency and the second vibration frequency. In yet anotheralternate embodiment, the processing routine 210 can sweep the vibrationof the driver 104 between the first vibration frequency 211 and thesecond vibration frequency 212, wherein the actual drive frequency isstepped between the two frequencies according to the sweep time period215.

FIG. 3 is a flowchart 300 of a method for determining flowcharacteristics in a Coriolis flow meter 5 according to an embodiment ofthe invention. In step 301, the flow tube apparatus 10 is vibrated withthe first vibration frequency 211 and in a first out-of-phase bendingmode by the driver 104. The first vibration frequency 211 can be afundamental vibration frequency of the flow meter assembly 10, or can bea frequency above or below the fundamental frequency.

In step 302, the first vibrational response 213 is measured. Themeasurement comprises receiving signals from the pick-offs 105 and usingthe pick-off signals to determine the phase difference between the twopick-offs 105. The first vibrational response 213 is generated by theflow meter assembly 10 in response to the first vibration frequency 211generated by the driver 104.

In step 303, the flow meter assembly 10 is vibrated with a secondvibration frequency 212 and in the first out-of-phase bending mode bythe driver 104. The second vibration frequency 212 can be any frequencythat is not the first vibration frequency 211. In one embodiment, thefirst and second vibration frequencies 211 and 212 are substantiallyequally spaced above and below a fundamental frequency of the flow meterassembly 10. However, as was previously noted, the first and secondvibration frequencies 211 and 212 can comprise any desired frequencies.

In step 304, a second vibrational response 214 is measured. The secondvibrational response 214 is generated by the flow meter assembly 10 inresponse to the second vibration frequency 212 generated by the driver104.

In step 305, the mass flow rate and other flow characteristics aredetermined by the meter electronics 20 from the first and secondvibrational responses 213 and 214. By collecting two or more vibrationalresponses, the meter electronics 20 can determine many flowcharacteristics. The flow characteristics can include the density 221,the kinematic viscosity 222, the dynamic viscosity 223, the shear rate224, the Reynolds number 225, the VOS 226, and the damping factor 227 ofthe flow material in the flow meter assembly 10.

The vibrating structure of a Coriolis flow meter 5 can be described as asingle degree of freedom resonator that obeys the differential equation:dx ² /dt ²+2ζdx/dt(t)+ω² _(n) x(t)=ω² _(n) A cos(ωt)  (1)where the right hand side represents the normalized oscillatory forcingfunction and ζ is the damping factor. Here, x is an instantaneous flowtube displacement and the terms dx/dt and dx²/dt² are first and secondorder derivatives of the displacement, respectively.

The frequency response of this system is given by:G(ω)=1/(1−(ω/ω_(n))² +j2ζω/ω_(n))  (2)with a magnitude response of:|G(ω)|²=1/([1−(ω/ω_(n))²]²+(2ζω/ω_(n))2)  (3)and with a phase response φ of:φ(ω)=tan⁻¹2ζω/ω_(n)/(1−(ω/ω_(n))²)  (4)

FIG. 4A shows magnitude response characteristic curves for threedifferent values of the damping factor ζ, while FIG. 4B shows the threecorresponding phase response characteristic curves. The three curvesreflect damping factors of ζ=0.05, ζ=0.1, and ζ=0.2. Therefore, it canbe seen from the graph that the damping factor ζ can be correlated toand derived from the phase and magnitude of the vibrational responsesover at least two frequencies ω₁ and ω₂.

The purity of the resonator's sustained oscillation is captured in thequality factor Q, which is defined as:Q=|G(ω)|_(max)  (5)where the quality factor Q is equivalent to the damping factor ζ.

For lightly damped systems (i.e., where ζ<<1), it can be shown that:Q≈½ζ≈ω_(n)/(ω₂−ω₁)  (6)where ω₁ and ω₂ are the half power points at which an amplitude responsefor the flow meter assembly 10 falls to a value of (Q/√(2)). Thequantity:Δω=ω₂−ω₁  (7)is also known as the 3 dB bandwidth of the system. Note that generallythe point of maximum response ω₀ is given by:ω₀=ω_(n)√(1−2ζ²)  (8)indicating that the maximum response ω₀ occurs at a frequency lower thanthe undamped natural frequency ω_(n).

The dynamic viscosity (v) of a flow medium passing through a Coriolismass flow meter will directly alter the structure's quality factor Q.The more viscous the flow medium, the more damped the system. Indeed,the dynamic viscosity v of the flow medium and the quality factor Q arerelated by:Q=K _(v)/√(v)  (9)where K_(v) is a proportionality constant that is divided by the squareroot of the viscosity v. This suggests that a method that enables theflow meter 5 to measure the system's damping factor ζ (or equivalentlyits quality factor Q) will yield the dynamic viscosity v, afterappropriate calibration.

There are a number of methods that can be used to determine the qualityfactor Q. A first method measures the quality factor Q directly asdefined by equation (5) by measuring the peak amplitude |G(ω)|_(max). Todo this, the flow meter assembly 10 can be driven open loop through acontinuum of drive frequencies encompassing ω₀. This is done whilemaintaining the drive power constant, as a means of normalization. Thedifficulty with this approach is that it requires some type of absoluteamplitude response calibration, which can be noisy and inaccurate anddoes not account for the variability of pickoff efficiency.

A second method drives the flow conduit or conduits to their nominaldisplacement amplitude and periodically disengages the driving forcewhile monitoring the oscillation's amplitude decay. The time taken forthe amplitude to decrease to 0.707 of its peak value will provide analternate measure of the quality factor Q. The difficulties encounteredwith this method stem from the discontinuous nature of the drivingfunction, which will instantaneously and periodically perturb thequality of the mass flow rate measurement.

A third method measures the quality factor Q of the flow meter assembly10 by driving the flow meter assembly 10 successively at the half powerpoints ω₁ and ω₂ and at the point of maximum response ω₀. This is anattractive approach because the quality factor is totally dependent onthe mechanical properties of the resonator, and is not dependent on theefficiency of the driver 104 or on the efficiency of the pick-offs 105.The difficulty with this approach is that when the flow meter assembly10 is switched from one frequency to another (such as from ω₁ to ω₀),the flow meter assembly 10 will be disrupted and will need time tosettle back into its stable regime. During this settling period, allprocess information (viscosity, density, and mass flow rate) can be lostor the measurement quality can be seriously degraded.

The invention provides a substantially continuous and uncompromisedmeasurement of at least mass flow rate, density, and viscosity.

FIG. 5 shows a feedback loop for controlling a vibration frequencyapplied to the flow meter assembly 10. The feedback loop can include theCoriolis sensor 500 (i.e., the flow meter 5), a phase shifter 501, adigital-to-analog (D/A) converter 502, an analog-to-digital (A/D)converter 503, and a phase sensor 504. In operation, the phase shifter501 generates a digital drive signal that is converted to an analogdrive signal by the D/A 502 and provided to the Coriolis sensor 500. Thepickoff signal output is provided to the A/D 503, which digitized theanalog pickoff signal and provides it to the phase shifter 501. Thephase sensor 504 compares the input (drive) phase to the output (sensor)phase, and generates a phase difference signal to the phase shifter 501.As a result, the phase shifter 501 can control the phase shift and thefrequency of the drive signal provided to the Coriolis sensor 500.

As shown in the figure, the invention controls the phase between thesensor's input and output so as to continuously cycle the closed-loopresonance between first and second vibration frequencies ω₁ and ω₂ whilemaintaining the system under closed-loop control. Such phase control canbe digitally implemented using standard phase-locked loop techniques. Inone embodiment, the closed-loop control can be performed by anappropriately programmed Digital Signal Processor (DSP). However, otherfeedback or loop control techniques can be employed and are within thescope of the description and claims.

The target phase setpoint shown in FIG. 5 is a periodic function of timesuch as:φ(t)=φ₀+Δφ sin(2πt/T _(φ))  (10)with the phase modulation index Δφ and the modulation period T_(φ) beingon the order of several seconds in one embodiment. With such a slowlyvarying phase variation, the system closed-loop oscillating frequencywill track continuously as predicted by the phase curve shown in FIG.4B. Therefore, for every period of time T_(φ), all relevant variables(ω₀, ω₁, ω₂, and mass flow rate) can be measured by tracking therelative amplitude response throughout the continuum of operating pointsω_(E)[ω₁, ω₂], with no need for absolute calibration of the amplituderesponse.

Depending on the response time required, the density ρ can be determinedin various ways. For example, in one embodiment the density ρ can bedetermined by periodically updating the density output each time thephase passes through the density calibration phase point ρ_(cal). Inanother embodiment, the density ρ is dynamically determined by applyinga frequency correction factor, wherein the frequency correction factoris dependent on the actual phase and on the viscosity of the product.

The shear rate 224 can be determined by utilizing the mass flow rate 220through the flow meter assembly 10 and from the natural resonantfrequency of the flow meter assembly 10. Consequently, by changing theflow rate and/or by changing the resonant frequency of the flow meter 5by operating in a different mode of vibration, the shear rate 224 can bemodified. This capability leads to the ability to profile non-Newtonianor liquid products substantially instantaneously. Fluids for which theshearing stress is linearly related to the rate of shearing strain aredesignated as being Newtonian fluids. Newtonian materials are referredto as true liquids, since their viscosity or consistency is not affectedby shear, such as agitation or pumping at a constant temperature.Fortunately, most common fluids, both liquids and gases, are Newtonian,including water and oils.

The Reynolds number R_(e) 225 for the flow medium can be determined fromthe three prime measurements that are simultaneously measured by theflow meter assembly 10, i.e., the Reynolds number R_(e) 225 can bedetermined from the mass flow rate 220, the density 221, and from thedynamic viscosity 223.

The vibrational responses generated by the Coriolis flow meter 5 canadditionally be used for other purposes. For example, in one embodiment,the two or more vibrational responses can be used to determine aflexural stiffness of the flow meter assembly 10. The flexural stiffnesscan be used in order to correct a Flow Calibration Factor (FCF) based ona stiffness change.

Factors that affect flexural stiffness also affect Coriolis flow metersensitivity (flow calibration factor). Flexural stiffness is the staticspring rate derived from flexing the flow tube with a known forcepattern and measuring the flow tube displacement. Any force patterncould be used to measure flexural stiffness, as long as it is invariant.As an example, the flexural stiffness for a clamped beam is as follows:

$\begin{matrix}{K_{Flex} = {\frac{F}{\delta} = \frac{192\;{EI}}{L^{3}}}} & (11)\end{matrix}$where:

F—Force (N);

E—Young's Modulus (N/m²);

I—Moment of Inertia (m⁴);

L—Length (m);

K_(flex)—flexural stiffness of flow tube.

For a Coriolis flow meter, if flexural stiffness changes, then so mustthe calibration factor change. Flexural stiffness of a Coriolis flowmeter is defined as:K_(flex)=C_(P)C_(G)C_(S)[EI]  (12)where:

C_(P)—effect of force pattern on flexural stiffness;

C_(G)—effect of unflexed tube bend geometry on flexural stiffness;

C_(S)—effect of unflexed tube stress on flexural stiffness.

For a straight tube Coriolis flow meter with no pre-stress, thefollowing expressions show the dependence of calibration factor on EI:

$\begin{matrix}{\overset{.}{m} = {{C\left\lbrack \frac{EI}{L^{3}} \right\rbrack}\Delta\; T}} & (13)\end{matrix}$So the flow calibration factor (FCF) for the straight tube is:

$\begin{matrix}{{FCF} = {C\left\lbrack \frac{EI}{L^{3}} \right\rbrack}} & (14)\end{matrix}$where C is a constant determined by mode shape and pick-off locations.

Flow tube flexural stiffness can also be determined by estimating pointson a tube frequency response function (FRF) at given frequencies. Thesepoints are then used to fit a single degree of freedom model to the dataand determine the DC (e.g. zero crossing) point on the FRF.

A flow calibration factor can be validated using a multiple frequencyestimation process. Multiple frequency estimation begins by identifyingconstants m₁, c₁, k₁, ζ₁, ω₁, and A₁ using any time domain or frequencydomain system identification method. A curve fitting procedure is usedto fit a rational continuous time transfer function model to the complexfrequency response vector H at the set of frequencies in vector W (inradians/second). The number and location (in frequency) of the FRF datapoints does affect the quality of the fit. A good fit is achieved usingas few as 2 frequency response data points. The derived model is of theform:

$\begin{matrix}{{H(s)} = \frac{{{b(1)}s^{N_{b}}} + {{b(2)}s^{({N_{b} - 1})}} + \ldots + {b\left( {N_{b} + 1} \right)}}{s^{N_{b}} + {{a(2)}s^{({N_{a} - 1})}} + \ldots + {a\left( {N_{a} + 1} \right)}}} & (15)\end{matrix}$

The driver pickoff mobility (velocity) frequency response data isconverted to the receptance (displacement) form. The measured mobilityfrequency response data H must be multiplied by 1/(iω). The measuredmobility drive loop frequency response H should be from drive coilcurrent (proportional to force) to pickoff voltage (proportional tovelocity).

Converting the mobility data to receptance data yields H(s) in the form:

$\begin{matrix}{{H(s)} = \frac{b(1)}{{{a(1)}s^{2}} + {{a(2)}s} + {a(3)}}} & (16)\end{matrix}$where a(1)=1. The modal parameters of interest are extracted from thetransfer function model as follows:

$\begin{matrix}{{A_{1} = {b(1)}}{\omega_{1} = \sqrt{a(3)}}{\zeta_{1} = {{{a(2)}/2}/\omega_{1}}}} & (17)\end{matrix}$The physical parameters can then be calculated using the followingequations:m ₁=1/A ₁c ₁=2ζ₁ω₁ /A ₁k ₁=ω₁ ² /A ₁  (18)

Once the physical parameters are determined, changes in the flowcalibration factor, as well as other parameters (including changes inthe mass and length of the flow tube), are determined and corrected.

In an additional capability, the two or more vibrational responses canalso be used to detect and differentiate flow meter structure changes,such as erosion, corrosion, and coating of the flow tube. In one suchembodiment, the Coriolis flow meter 5 is vibrated at its resonantfrequency so as to enable flow meter 5 to measure mass and density. Themass measurement is based on the following equation:

=FCF*[Δt−Δt ₀]  (19)Where:

is the mass flow rate;

FCF is the flow calibration factor;

Δt is the time delay; and

Δt₀ is the time delay at zero flow.

The FCF term is proportional to the stiffness of the flow meter.Stiffness is the predominate parameter that affects the flow meter'sperformance. If the stiffness of the flow meter changes, then themeter's FCF will change. A change in the flow meters performance can becaused by corrosion, erosion, and coating, for example.

Equation (19) can be rewritten to reflect the stiffness:

=G*(EI)*[Δt−Δt ₀]  (20)Where:

G is a geometric constant associated with a particular sensor;

E is Young's Modulus; and

I is the moment of inertia.

The area moment of inertia, I, changes when the meter's flow tubechanges. For example, if the tube corrodes reducing the wall thickness,the area moment of inertia is decreased.

In one embodiment, the invention includes a process for detecting anddifferentiating flow meter structure changes from indicated changes inflow rate. The process starts with the determination of mass flow rate,

, using multiple modes and the following equation:

$\begin{matrix}{\begin{pmatrix}m_{1}^{o} \\m_{2}^{o} \\m_{n}^{o}\end{pmatrix} = {{{E\begin{pmatrix}G_{1} & \; & \; \\\; & G_{2} & \; \\\; & \; & G_{n}\end{pmatrix}}\begin{pmatrix}I_{1} & \; & \; \\\; & I_{2} & \; \\\; & \; & I_{n}\end{pmatrix}\begin{pmatrix}{\Delta\; t_{1}} & \; & \; \\\; & {\Delta\; t_{2}} & \; \\\; & \; & {\Delta\; t_{n}}\end{pmatrix}} - \begin{pmatrix}{\Delta\; T_{1\; o}} \\{\Delta\; t_{2\; o}} \\{\Delta\; t_{no}}\end{pmatrix}}} & (21)\end{matrix}$

When multiple modes are excited, either from flow noise or forcedvibration, the vibration of the mode will couple with the mass flowpassing through the flow tube, causing a Coriolis response for eachmode. The Coriolis response results in an associated Δt which is used tocalculate a mass flow reading for each mode.

The mass flow reading for each mode is compared. The resulting mass flowrate must be the same for each mode. If the mass flow readings areequal, the comparison generates a “proper operation” signal and theprocess restarts. The “proper operation” signal can be in the form of avisible or audible signal to a user, for example.

When a deviation occurs between the mass flow rates, which are outsideof acceptable limits, an error signal is generated. The error signal cancause various actions to occur. For instance, the error signal may causethe process to be shut down or may signal a visible or audible warningto an operator who then takes appropriate action.

The density measurements of the Coriolis meter 5 are based on thefollowing equation:

$\begin{matrix}{{2\;\pi\; f} = {\frac{2\;\pi}{\tau} = \sqrt{\frac{k}{m}}}} & (22)\end{matrix}$Where:

k is the stiffness of an assembly;

m is the mass of the assembly;

f is the frequency of oscillation; and

τ is the period of oscillation

Equation (22) is the solution of the equation of motion for a singledegree-of-freedom system. A Coriolis flow meter at zero flow isrepresented by an expansion of equation (22), yielding:

$\begin{matrix}{\frac{2\;\pi}{\tau} = \sqrt{\frac{{EIG}_{\rho}}{{\rho_{f}A_{f}} + {\rho_{t}A_{t}}}}} & (23)\end{matrix}$Where:

E is Young's modulus;

I is the cross-sectional moment of inertia;

G_(p) is a geometric constant;

A is the cross-sectional area;

ρ is the density

f represents the fluid in the flow meter; and

t represents the material of the flow tube(s).

By rearranging terms, equation (23) can be re-written as:ρ_(f) =C ₁τ² −C ₂  (24)Where:

$\begin{matrix}{{C_{1} = {G_{\rho}\frac{EI}{4\;\pi^{2}A_{f}}}},} & (25) \\{and} & \; \\{C_{2} = \frac{\rho_{t}A_{t}}{A_{f}}} & (26)\end{matrix}$The geometric constant, G_(p), accounts for geometric parameters such astube length and shape. The constants, C₁ and C₂, are determined as partof the normal calibration process at zero flow on two different fluids.

In one embodiment, the invention includes a process for detecting anddifferentiating flow meter structure changes from changes in indicateddensity. The process starts with the determination of density, ρ, usingmultiple modes. Multiple modes can be excited either from flow noise orforced vibration.

The density readings for each mode are compared. The resulting densityreading must be the same for each mode. If the density readings areequal, the process generates a “proper operation” signal and the processrestarts. The “proper operation” signal can be in the form of a visibleor audible signal to a user.

When a deviation occurs between the density readings, which are outsideof acceptable limits, an error signal is generated. The error signal cancause various actions to occur. For instance, the error signal may causethe process to be shut down or may signal a visible or audible warningto an operator who then takes appropriate action.

The Coriolis flow meter and method according to the invention can beemployed according to any of the embodiments in order to provide severaladvantages, if desired. The invention provides a flow meter that iscapable of measuring various flow characteristics. The inventionmeasures the flow characteristics using at least first and secondvibration frequencies to excite the flow meter assembly. The inventionadvantageously operates a Coriolis flow meter to provide additionalmeasurements of dynamic viscosity, kinematic viscosity, and densitywithout compromising the mass flow measurement performance of the flowmeter. The invention can additionally provide shear rate, Reynoldsnumber, VOS, and damping factor values. These various flowcharacteristics advantageously give more detailed and explicitinformation on the makeup and behavior of the flow medium.

There are numerous applications in virtually all the major industriesfor a product which simultaneously measures mass flow, density, andviscosity. In one example, the invention can be used for ship fuel oilblending, wherein kerosene is blended with fuel oil to a given kinematicviscosity specification. The resulting blend can be concurrently meteredonto a ship. In order to provide a solution to this application, themass flow rate, the density, and the viscosity measurements arerequired.

In another example, the invention can be used for lube oil drum filling.Many different lube oils exist, and they are typically manufactured in asingle stream and batch filled into drums. During batch filling ofdrums, the interface between the different lube oil products must beaccurately detected in order to prevent contamination. The interface isdetected through a change in product viscosity using the viscositymeasurement provided by the invention. The mass flow output is used toaccurately batch fill the drums using the mass flow rate measurementprovided by the invention.

In another example, the invention can be used for receiving highfructose corn syrup (HFCS) solutions, such as HFCS-55, for example.During the receiving of HFCS solutions, each solution will have aspecific density (in Brix) and viscosity quality specification. Brix hasbeen defined as a measure of the percentage of solids in a plant juiceor alternatively as a measure of percentage of sucrose (sugar). Clearly,having the ability to measure these quality parameters simultaneouslywith the mass flow rate is a major benefit to the customer.

1. A Coriolis flow meter (5) comprising one or more flow conduits (103),at least two pickoff sensors (105, 105′) affixed to the one or more flowconduits (103), and a driver (104) configured to vibrate the one or moreflow conduits (103), with the Coriolis flow meter (5) beingcharacterized by: meter electronics (20) coupled to the at least twopickoff sensors (105, 105′) and to the driver (104), with the meterelectronics (20) being configured to vibrate the one or more flowconduits (103) of the flow meter with a first vibration frequency and ina first out-of-phase bending mode, measure a first vibrational responseof the one or more flow conduits (103), with the first vibrationalresponse being generated in response to the first vibration frequency,vibrate the one or more flow conduits (103) with at least a secondvibration frequency and in the first out-of-phase bending mode, measurea second vibrational response, with the second vibrational responsebeing generated in response to the second vibration frequency, anddetermine at least a mass flow rate and a viscosity using the firstvibrational response and the second vibrational response.
 2. TheCoriolis flow meter (5) of claim 1, with the determining furthercomprising determining a density.
 3. The Coriolis flow meter (5) ofclaim 1, with the determining further comprising determining a shearrate.
 4. The Coriolis flow meter (5) of claim 1, with the determiningfurther comprising determining a Reynolds number.
 5. The Coriolis flowmeter (5) of claim 1, with the determining further comprisingdetermining a velocity of sound (VOS).
 6. The Coriolis flow meter (5) ofclaim 1, with the determining further comprising determining a pressure.7. The Coriolis flow meter (5) of claim 1, with the viscosity comprisinga kinematic viscosity.
 8. The Coriolis flow meter (5) of claim 1, withthe viscosity comprising a dynamic viscosity.
 9. The Coriolis flow meter(5) of claim 1, further comprising jumping between the first vibrationfrequency and the second vibration frequency.
 10. The Coriolis flowmeter (5) of claim 1, further comprising substantially simultaneouslyvibrating the one or more flow conduits (103) with the first vibrationfrequency and the second vibration frequency.
 11. The Coriolis flowmeter (5) of claim 1, further comprising sweeping between the firstvibration frequency and the second vibration frequency over apredetermined sweep time period.
 12. The Coriolis flow meter (5) ofclaim 1, with the first vibration frequency and the second vibrationfrequency being substantially equally spaced above and below afundamental frequency of the one or more flow conduits (103).
 13. TheCoriolis flow meter (5) of claim 1, with the one or more flow conduits(103) comprising two, substantially U-shaped flow conduits.
 14. A methodfor determining flow characteristics n a Coriolis flow meter, comprisingvibrating one or more flow conduits of the flow meter with a firstvibration frequency and in a first out-of-phase bending mode andmeasuring a first vibrational response of the one or more flow conduits,with the first vibrational response being generated in response to thefirst vibration frequency, with the method being characterized by:vibrating the one or more flow conduits with at least a second vibrationfrequency and in the first out-of-phase bending mode; measuring a secondvibrational response, with the second vibrational response beinggenerated in response to the second vibration frequency; and determiningat least a mass flow rate and a viscosity of the flow medium using thefirst vibrational response and the second vibrational response.
 15. Themethod of claim 14, with the determining further comprising determininga density.
 16. The method of claim 14, with the determining furthercomprising determining a shear rate.
 17. The method of claim 14, withthe determining further comprising determining a Reynolds number. 18.The method of claim 14, with the determining further comprisingdetermining a velocity of sound (VOS).
 19. The method of claim 14, withthe determining further comprising determining a pressure.
 20. Themethod of claim 14, with the viscosity comprising a kinematic viscosity.21. The method of claim 14, with the viscosity comprising a dynamicviscosity.
 22. The method of claim 14, further comprising jumpingbetween the first vibration frequency and the second vibrationfrequency.
 23. The method of claim 14, further comprising substantiallysimultaneously vibrating the one or more flow conduits with the firstvibration frequency and the second vibration frequency.
 24. The methodof claim 14, further comprising sweeping between the first vibrationfrequency and the second vibration frequency over a predetermined sweeptime period.
 25. The method of claim 14, with the first vibrationfrequency and the second vibration frequency being substantially equallyspaced above and below a fundamental frequency of the one or more flowconduits.
 26. A Coriolis flow meter software product for determiningflow characteristics in a Coriolis flow meter, comprising a controlsoftware on a computer readable medium configured to direct a processingsystem to vibrate one or more flow conduits of the flow meter with afirst vibration frequency and in a first out-of-phase bending mode,measure a first vibrational response of the one or more flow conduits,with the first vibrational response being generated in response to thefirst vibration frequency, and a storage system that stores the controlsoftware, with the software product being characterized by: the controlsoftware being further configured to direct the processing system tovibrate the one or more flow conduits with at least a second vibrationfrequency and in the first out-of-phase bending mode, measure a secondvibrational response, with the second vibrational response beinggenerated in response to the second vibration frequency, and determineat least a mass flow rate and one or more flow characteristics using thefirst vibrational response and the second vibrational response.
 27. Thesoftware product of claim 26, with the determining further comprisingdetermining at least a density and a viscosity of the flow medium. 28.The software product of claim 26, with the determining furthercomprising determining a shear rate.
 29. The software product of claim26, with the determining further comprising determining a Reynoldsnumber.
 30. The software product of claim 26, with the determiningfurther comprising determining a velocity of sound (VOS).
 31. Thesoftware product of claim 26, with the determining thither comprisingdetermining a pressure.
 32. The software product of claim 26, with theviscosity comprising a kinematic viscosity.
 33. The software product ofclaim 26, with the viscosity comprising a dynamic viscosity.
 34. Thesoftware product of claim 26, further comprising jumping between thefirst vibration frequency and the second vibration frequency.
 35. Thesoftware product of claim 26, further comprising substantiallysimultaneously vibrating the one or more flow conduits with the firstvibration frequency and the second vibration frequency.
 36. The softwareproduct of claim 26, further comprising sweeping between the firstvibration frequency and the second vibration frequency over apredetermined sweep time period.
 37. The software product of claim 26,with the first vibration frequency and the second vibration frequencybeing substantially equally spaced above and below a fundamentalfrequency of the one or more flow conduits.